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I have an irrational hope that since the shape of the actual universe is a scaled 4-sphere, for which the Dirac spectrum are integers, there might be a special information regarding number theory.  The behavior of $\zeta(s)$ for $s=-1/2$ are interesting for Riemann hypothesis.  In the geometric side, this is related to the Casimir effect:  KirstenZetaFunctionsDiracLaplacCylinders.